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Imaging of primaries and multiples using a dual-sensor towed streamer
N. D. Whitmore*, A.A. Valenciano, and Walter Sollner, PGS, Shaoping Lu, University of Texas
Summary
Multiple reflections are commonly treated as noise in oneway imaging methods. High effort is put into research and
data processing worldwide in an effort to suppress this
source of noise. In a new perspective multiples are treated
as valuable imaging information. Based on dual-sensor
towed streamer measurement, we decompose the wavefield
and apply up/down imaging of primary and multiple
reflections. This approach is tested using shallow water
synthetic data and finally applied on dual-sensor field data.
generating boundaries need to be known in this approach
before starting the imaging process. Berkhout and
Verschuur (1994) and Guitton (2002) use one-way
wavefield extrapolation for migrating surface-related
multiples after explicitly separating from the data. In this
case, the multiples are inverse extrapolated and the
recorded data is forward extrapolated after multiplying with
-1 (the reflection coefficient for calm sea). Muijs et al.
(2007) employ OBC wavefield decomposition to migrate
primaries and multiples in one step. This relates to the
up/down imaging approach (Claerbout, 1976) and is not
restricted to calm sea conditions.
Introduction
Conventional depth imaging by one-way wavefield
extrapolation is based on the assumption that measured data
represents an upward propagating primary reflected
(scattered) wavefield. This assumption is solely fulfilled if
the free-surface effects such as receiver ghosts, surface
related multiples, and internal multiples are effectively
suppressed.
Deghosting of seismic data is a nontrivial procedure, even
for a flat sea surface and reflection coefficient of -1
(Ghosh, 2000). In order to move the spectral notches
caused by receiver ghosts out of the main part of signal
bandwidth, hydrophones are typically towed shallow in
marine data acquisition. In recent years attempts have been
made to introduce techniques for rough sea deghosting by
using sea surface profile information (Amundsen, 2005).
Kragh et al. (2002) derive the needed sea surface profile
from very low frequency pressure fluctuations and Orji et
al. (2009) image the sea-surface from below, using the
decomposed wavefields of dual-sensor towed streamer data
(Carlson, et al., 2007).
In this work we adapt the up/down imaging approach of
primaries and multiples to a dual-sensor towed streamer
system by keeping the relaxed sea-surface condition.
Shot –profile wave-equation imaging conditions
In shot-profile wave-equation migration, an approximation
of the reflection coefficient is given by (Claerbout, 1971)
I1 (x)
xs
From a different perspective, multiples may be treated as
valuable information and as such be included in new
imaging algorithms. Reiter et al., 1991 use a Kirchhoff
approach to image water layer multiples. The two multiple
© 2010 SEG
SEG Denver 2010 Annual Meeting
1
where x = (x,y,z) is each image position, is the angular
frequency, and xs = (xs,ys,zs) is each source position. R and
S denote the receiver and source wavefields, respectively.
Physically, equation 1 states that a reflector exists where R
and S coincide in time and space. Equation 1 will be
numerically unstable wherever S equals (or is close to)
zero. For this reason, it is customary to multiply both the
numerator and the denominator by the complex conjugate
of S (i.e. S’) and add a stabilization parameter as follows:
S' x,x s ; R x,x s ;
S' x,x s ; S x,x s ;
I2 (x)
xs
Removing the sea surface effects is the ultimate goal of
SRME (Verschuur et al., 1991, Berkhout and Verschuur,
1997) and related methods of surface-related multiple
suppression (Carvalho et al., 1991; Fokkema and van den
Berg, 1993; van Borselen et al., 1996; Amundsen, 2001,
Ikelle et al., 2003). Common feature of these methods is the
independency of parameters characterizing the subsurface
model. Söllner et al., 2007 and Frijlink et al., 2009 employ
separated wavefields of a dual-sensor streamer in order to
relax the sea surface assumption of SRME. However, the
time varying sea-surface is not included in this concept.
R x,x s ;
S x,x s ;
2
(2)
We call equation 2 the damping imaging condition. Note
that equation 2 is equivalent to equation 1 multiplied by an
optimal Wiener filter, assuming that the spectrum of the
noise is white. Equation 2 poses a serious problem to
practitioners: how do we estimate the damping parameter
? Since stability is often more important than
mathematical accuracy, the imaging condition is usually
implemented by using crosscorrelation between R and S as
follows:
I3 (x)
S' x,x s ;
R x,x s ;
(3)
xs
We call equation 3 the crosscorrelation imaging condition.
Jacobs (1982) analyzes in detail the differences between
equations 3 and 2.
Guitton et al. (2007) proposed approximating the
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Imaging of primaries and multiples
deconvolution imaging condition in equation 2. The main
goal of their method is to emulate the deconvolution while
being practical and robust filling the zeros in the
denominator in equation 2. Therefore, they proposed the
following:
I4 (x)
xs
S' x,x s ; R x,x s ;
S' x,x s ; S x,x s ;
(4)
traveling direct arrival, if recorded. PD and PU are the
separated down and up going data derived from deghosting
the dual-sensor components. When we include wavefield
extrapolation in the wavefield separation process, the
source and receiver depths and be chosen at a z=0 or a
depth equal to or greater than the cable depth, to avoid the
effects of a rough sea surface.
x,y
where (x,y,) stands for smoothing in the image space in the
x,y directions. Equation 4 was called the smoothing
imaging condition. In this paper, a triangle function is used
as the smoothing function. Valenciano et al. (2003), and
Muijs et al. (2007) discussed the use of more dimensions in
the imaging condition; but the computational cost the
extension required makes it less attractive in a production
environment. This method is used as the deconvolution
imaging condition in the examples below.
Up/Down Decomposition
Up/Down Extrapolation
PD
PD
zR
zR
PU
PU
Imaging of primaries and multiple reflections
Equations 1 to 4 can be used to image either primaries or
multiples depending on the data used to fill the boundary,
at z = 0, for the receiver and the source wavefields
(Verschuur and Berkhout, 1995; Guitton, 2002; Shan,
2003; Berkhout and Verschuur, 2006; Muijs et al. 2007).
For imaging of primaries, a point (or areal) source is used
as the boundary condition; for imaging of multiples a
generalized source is necessary.
Dual-sensor data consisting of pressure and vertical
velocity sensors is decomposed at a predefined horizontal
datum in up going and down going pressure fields
(Claerbout, 1976; Fokkema and van den Berg, 1993;
Carlson, 2007). The separation level serves as initial
boundary condition for imaging the primaries and multiple
reflections, as sketched in Figure 1. Based on the concept
that every up going wave branch is generated from a
forward propagated down going wave branch, we use the
direct down going wavefield for imaging the primaries and
the scattered down going wavefield for imaging all surface
related multiples.
In this paper we compare the results of using different
imaging conditions, and different data as boundary
condition for the source wavefield
S( x, y, z
zS , xs ; )
S D ( x, y , z S , x s ; )
D
(5.1)
P ( x, y, z S , x s ; )
(5.2)
P ( x, y, z R x s ; )
(6.1)
and the receiver wavefields,
R( x, y, z
zR , xs ; )
U
P ( x, y, z R , x s ; )
(6.2)
When imaging primaries, SD can be a point source with a
specified frequency domain wavelet or the downward
© 2010 SEG
SEG Denver 2010 Annual Meeting
Figure 1: Up Down Separation and Extrapolation
Shallow water Sigsbee2B example
The Sigsbee2B model simulates the geological setting
interpreted at the Sigsbee escarpment in the deep-water
Gulf of Mexico. The model was designed to test surfacerelated demultiple algorithms, thus a free surface boundary
condition was used. In addition, a “hard” water bottom was
included in the velocity model.
Since our interest is to use the multiples and not remove
them we created a new dataset with similar geometry to the
original SMAART distribution. The goal was to record in
the new model data as many orders of multiples as possible
in a 12 seconds recording time. To achieve that goal, we
stripped 5000 feet of the water column from the velocity
model (Figure 2).
For this model we tested imaging of primaries and
multiples - with both crosscorrelation and deconvolution
imaging conditions. For example, Figure 3 shows an
example of typically employed imaging process for
primaries with a deconvolution imaging condition: the
source field was an analytical point source with a flat
spectrum and the receiver field was initiated by injecting
the total pressure at the surface as described in equations
(5.1) and (6.1). This image can be compared with a
multiple image generated from deconvolution imaging
conditions. In this example, the multiple image was
generated by downward continuing PD as the source field
and PU as the receiver field, as described in equations (5.2)
and (6.2) and then applying deconvolution imaging
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Imaging of primaries and multiples
conditions. The results are shown in Figure 4. Note that the
structural image from primaries and multiples are similar.
However, the basic wavelets of the images are different
This is is due to the fact that the primary image was
generated with a flat spectrum and that P-total has a
different spectrum than the P-up.
This demonstrates that the primaries and multiples can be
imaged. However, it is important to properly incorporate
the source wavelet when comparing or perhaps combining
primary and multiple images.
North Sea dual-sensor streamer example
The second application for the imaging of primaries and
multiples uses a 3D data set from the North Sea acquired
with dual-sensor streamers comprised of hydrophones and
vertical geophones. Dual-sensor deghosting and
extrapolation was applied to these data to produce upgoing
and downgoing pressure. A subset of upgoing pressure
shot records are shown in Figure 5.
Figure 2: "Shallow Water" Sigsbee2b Model
Figure 5: Representative Upgoing Pressure shot points
generated from dual-sensor deghosting – no multiple
attenuation has been applied.
Figure 3: Deconvolution Image of Primaries (P total)
Figure 4: Deconvolution Image of Multiples
© 2010 SEG
SEG Denver 2010 Annual Meeting
The original streamer depth for this data was 15 meters. As
it can be seen in the shot records, this data contains
significant short period and long period multiples. This is
due to a hard water bottom and other major impedance
changes. As a result, both the upgoing and downgoing
wavefields contain several orders of multiples. To address
the multiples when imaging the primaries, the upgoing data
is typically subjected to a cascade of short and long period
multiple removal (e.g. tau-p decon + surface SRME,
whereas the multiple imaging uses the multiples as signal.
Imaging of Primaries:
Imaging of the primaries was done for this data by
downward continuing and imaging the surface source and
receiver wavefields as defined by equations (5.1) and (6.1).
The source field is an analytical point source and the
receiver field is the upgoing P wavefield with a simple gap
decon applied to reduce some of the short period multiples.
The imaging condition was cross correlation. This primary
image with the velocity model is shown in Figure 6.
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Imaging of primaries and multiples
Figure 6; Primary Image - Cross Correlation
Figure 7: Multiple Image – Deconvolution
Imaging of Multiples:
The major complication in the imaging of multiples in this
data case is that the multiples in the data are very complex.
Because of this the imaging condition is critical in
obtaining a useful image of the multiples. As discussed
earlier to obtain a multiple image the downgoing pressure
and upgoing pressure are injected as the source and
receiver fields at datums as described in (5.2) and (6.2). We
applied two different imaging conditions – deconvolution
and cross correlation (equations 3 and 4) – and these results
are shown in Figures 7 and 8.
As can be seen from these results, the deconvolution
imaging condition produces an image comparable to the
primary image, while the cross-correlation image is riddled
with multiple reverberations. This indicates that the
deconvolution imaging condition was essential for the
imaging of multiples.
Conclusions
In this paper we have demonstrated the imaging of
primaries and multiples using dual-sensor data. The dualsensor data facilitates the proper separation of upgoing and
downgoing pressure at the acquisition surface. The imaging
process incorporates dual-streamer wavefield separation,
downwared extrapolation and the application of an imaging
condition. Cross correlation and smoothed deconvolution
imaging conditions were applied to both primaries and
multiples and the results were compared.
The deconvolution imaging conditions were essential in
producing a good images from the multiples, particularly in
the case of shallow to mid water depths with complex
multiples. Understanding of the effects of the source
© 2010 SEG
SEG Denver 2010 Annual Meeting
Figure 8: Multiple Image – Cross Correlation
wavelet and multiple generators are necessary for a direct
comparison of primary and multiple images. We treat
multiples not only as a source of noise that needs to be
removed, but also as a signal that can complement the
imaging of primaries.
Acknowledgements
The authors acknowledge PGS for the dual-sensor data and
permission to present this paper. We also acknowledge the
SMAART JV for the original Sigsbee2b model.
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